FisMat Seminar, May 15, 15:45

Massimo Moscolari. Aalborg UniversityTitle: Beyond Diophantine Wannier diagrams: gap labelling for Bloch-Landau HamiltoniansPlace: Pontificia Universidad Católica, Facultad de Matemáticas (Campus San Joaquin), Sala 5Abstract:In 1978 Wannier discovered a Diophantine relation expressing the integrated density of states of a gapped group of bands of the Hofstadter Hamiltonian as a linear function of the magnetic field flux with integer slope. I will show how to extend this relation to a gap labelling theorem for any 2D Bloch-Landau Hamiltonian operator and to certain non-covariant systems having slowly varying magnetic fields. The integer slope will be interpreted as the Chern character of the projection onto the space of occupied states. The talk is based on a joint work with H. Cornean and D. Monaco.